U.S. House Minority Leader Nancy Pelosi (D-CA) arrives to meet with House Democrats and U.S. Vice President Joseph Biden about a solution for the ''fiscal cliff'' on Capitol Hill in Washington January 1, 2013.

House Minority Leader Nancy Pelosi and pro-gay groups have urged San Francisco Archbishop Salvatore Cordileone not to attend the pro-traditional marriage "March for Marriage" event on Thursday in Washington, D.C, citing inclusive quotes by Pope Francis. The Vatican leader has repeatedly said, however, that he is not changing the definition of marriage as between one man and one woman.

"We share our love of the Catholic faith and our city of San Francisco," Pelosi wrote to Cordileone, in a letter obtained by the San Francisco Chronicle.

Pelosi, a Catholic, asked Cordileone not to participate in The National Organization for Marriage's "March for Marriage" event, which she claimed some of the participants show "disdain and hate towards LGBT persons."

She also quoted a famous remark by Pope Francis, which reads: "If someone is gay and is searching for the Lord and has good will, then who am I to judge him?" – A quote that made gay publication The Advocate name the Catholic leaders its person of the year in 2013.

Francis, however, has said that he upholds the teachings of the church.

"The teaching of the church, for that matter, is clear and I am a son of the church, but it is not necessary to talk about these issues all the time," Francis explained in a September 2013 interview.

He added that the catechism, or the Roman Catholic Church's official doctrine book, condemns homosexual acts, but called on the Church to love gays and lesbians, who "must be accepted with respect, compassion and sensitivity."

Cordileone has been an outspoken supporter for traditional marriage and has opposed attempts to change the legal definition of marriage to include same-sex couples. The Archbishop is chair of the Promotion and Defense of Marriage of the U.S. Conference of Catholic Bishops, and was a key petitioner for California's Proposition 8, which sought to ban same-sex marriage in 2008.

A number of pro-gay organizations including Faithful America have joined Pelosi in calling Cordileone to reconsider his position.

"This bishop in particular has really been very anti-gay and has really tried to divide this city around this issue," said Christine Haider-Winnett of Faithful America, according to ABC7 News. "We think that this is time for inclusion. Pope Francis, in particular, said 'who am I to judge' about gay people, really is calling us to be a church that welcomes all."

The Human Rights Campaign has also criticized Cordileone for agreeing to participate in an event alongside outspoken figures such as Bishop Harry Jackson, evangelical leader Jim Garlow and Heritage Foundation fellow Ryan Anderson, who have all made controversial comments on homosexuality.

US News pointed out, however, that Pope Francis' soft tone on such social issues has been seen as an "olive branch" to Catholics who support LGBT rights and same-sex marriage.

Christine Mugridge, director of communications for the Archdiocese of San Francisco, said that Cordileone's work "is intimately connected to the Catholic understanding that Pope Francis speaks about. There is nothing derogatory in the stances that the archbishop takes."

She added: "He is speaking in defense of the religious understanding of what marriage is, and then for the promotion of it. He is accepting opportunities on behalf of the Holy Father as his emissary in the Archdiocese of San Francisco, and he is obliged to defend the Catholic teaching on that."

In April, Christopher Plante of NOM told The Christian Post that the June 19 event is aimed at showing "the world, the media, members of Congress and the Supreme Court that the marriage debate is not over."

"There is a huge groundswell of popular support, popular belief in traditional marriage. And despite what the polls may say, the reality is the majority of Americans believe marriage is between one man and one woman," Plante added.